An Analytic Model of the Minimum-Average-B Levitron

An expansion model to the first order in r, which includes the toroidal correction, and which is feasible for analytical calculations, is derived in the curvilinear toroidal system of coordinates for the minimum-average-B levitron. Expansions, in powers of r, are derived for the current ring potential, the magnetic field components of the axisymmetric levitron, and the components of the perturbation of the magnetic field of the nonaxisymmetric levitron. Published analytical works treated the straight levitron's approximation which contains only the π and 2π resonances of the system. The advantage of this model is that it contains all the numerically observed resonances of the levitron.